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Extension of a Diophantine triple with the property \(D(4)\)

Acta Mathematica Hungarica volume 163, pages 213–246 (2021)Cite this article

Abstract

We give an upper bound on the number of extensions of a triple to a quadruple for the Diophantine m-tuples with the property D(4). We also confirm the conjecture of the uniqueness of such an extension in some special cases.

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Authors and Affiliations

  1. Faculty of Science, University of Split, Ruđera Boškovića 33, 21000, Split, Croatia

    M. Bliznac Trebješanin

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  1. M. Bliznac Trebješanin
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Correspondence to M. Bliznac Trebješanin.

Additional information

The author was supported by the Croatian Science Foundation under the project no. IP-2018-01-1313.

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Bliznac Trebješanin, M. Extension of a Diophantine triple with the property \(D(4)\). Acta Math. Hungar. 163, 213–246 (2021). https://doi.org/10.1007/s10474-020-01128-0

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  • DOI: https://doi.org/10.1007/s10474-020-01128-0

Key words and phrases

  • Diophantine tuple
  • Pell equation
  • reduction method
  • linear form in logarithms

Mathematics Subject Classification

  • 11D09
  • 11D45
  • 11J86